A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity? You need to use Gauss’s Law for this.

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gatorchia gatorchia · Answer 1 · 2019-10-01T13:19:30+02:00

Answer: the potental with twice larger radius 0.5* Vo ( being Vo =100V)

Explanation: In order to solve this proble, we know that teh potential due to charged sphere relative V=0 at infinity, we have

Vo=k*Q/R where R is the sphere radius

if we enlarge the radius to 2R the

V= k*Q/2*R = Vo/2

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okpalawalter8 okpalawalter8 · Answer 2 · 2022-04-25T18:21:54+02:00

The potential on the surface relative to infinity is mathematically given as

[tex]PD'=\frac{PD}{2}[/tex]

Question Parameter(s):

Conducting sphere is charged up such that the potential on its surface is 100 V If the sphere's radius were twice as large.

Generally, the equation for the potential difference at infinity is mathematically given as

[tex]PD=\frac{k*Q}{R}[/tex]

In conclusion, having a radius of two

[tex]PD'=\frac{k*Q}{2*R }[/tex]

Therefore

[tex]PD'=\frac{PD}{2}[/tex]